2. Simplifying trigonometric expressions often takes
some trial and error, but the following strategies may
be helpful:
Use algebra and fundamental identities to simplify the
expression.
Sometimes, writing all functions in terms of sines and
cosines may help.
Sometimes, combining fractions by getting a common
denominator may help.
Sometimes, breaking one fraction into two fractions may
help: a+b/c = a/c + b/c
Sometimes, factoring may help
3. Example:
tan x
sec x=
= sin x . cos x
cos x 1
= sin x
sin x
cos x
1
cos x
• tan x = sin x / cos x
• sec x = 1/ cos x
• To divide by a
fraction, multiply by
the reciprocal of the
denominator
• Reduce the
resulting product
ANSWER
4. Factor out a common factor of cos x
Use the identity: cos2 x = 1-sin2 x
Use a property of exponents to
multiply cos x and cos2 x
= cos x (1-sin2 x)
= cos x . cos2 x
= cos3 x
cos x – cos x sin2x
ANSWER
5. = sin x +cos x .
=
=
sin2 x + cos2 x
sin x sin x
cos x
sin x
• cot x = cos x / sin x
• Get a common
denominator of sin x
and add the two
fractions
• sin2 x + cos2 x =1
• csc x = 1/ sin x
sin2 x + cos2 x
sin x
1
sin x
csc x
=
=
sin x + cos x cot x
ANSWER
6. sec x – cos x
sec x
sec x
sec x
- cos x
sec x
=
= 1- cos2 x
= sin2 x
• a+b/c = a/c + b/c
• sec x divided by
itself is 1
• cos x/ sec x =
cos2 x
• 1- cos2 x = sin2 x
ANSWER
7. SIMPLIFYING THE FOLLOWING:
1. CSC X –SIN X
CSC X
2. SIN X + COS X
COS X 1+ SIN X
8. Give at least 3 examples of word problems
involving trigonometric expressions and
solutions. Write it in a whole sheet of paper
which will be submitted next meeting.
Good bye class!